Finite Group Databasebeta

← C2×#22613098 #33248592

Subgroups — C2×#22613098 #33248592

Order 18688.

2566 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556568C211yesmaximal, characteristic
2#22613098C2116yesmaximal, direct product factor
3C2×#17988493C211yesmaximal, characteristic, complemented
4C2×#17988491C211yesmaximal, characteristic, complemented
5C2×#17988484C211yesmaximal, characteristic, complemented
6C2×#17988483C211yesmaximal, characteristic, complemented
7C2×#17988481C211yesmaximal, characteristic
8C2×#17988481C211yesmaximal, characteristic
9C2×#17988480C211yesmaximal, characteristic
10C2×#17988472C211yesmaximal, characteristic, complemented
11C2×#17988471C211yesmaximal, characteristic, complemented
12C2×#17988469C211yesmaximal, characteristic, complemented
13C2×#17988468C211yesmaximal, characteristic, complemented
14C2×#17988448C211yesmaximal, characteristic
15C2×#17988445C211yesmaximal, characteristic
16C2×#388×C73C211yesmaximal, characteristic
17C23×Dic146C2211yescharacteristic
18C24×Dic73C2211yescharacteristic
19C2×#14556568C4116yescomplemented
20C2×#14556568C2218yes—
21C22×C4⋊Dic73C2211yescharacteristic
22C22×C4⋊Dic73C2211yescharacteristic
23C22×#11924007C2211yescharacteristic
24C22×#11924007C2211yescharacteristic
25C22×#11924007C2211yescharacteristic
26C22×#11924007C2211yescharacteristic
27C22×#11924007C2211yescharacteristic
28C22×#11924007C2211yescharacteristic
29C22×C22⋊Dic73C2211yescharacteristic
30C22×C22⋊Dic73C2211yescharacteristic
31C22×C22⋊Dic73C2211yescharacteristic
32C22×C4×Dic73C2211yescharacteristic
33C22×C4×Dic73C2211yescharacteristic
34C22×C4×Dic73C2211yescharacteristic
35#17988493C2218yescomplemented
36#17988491C2218yescomplemented
37#17988484C2218yescomplemented
38#17988483C2218yescomplemented
39#17988481C2218yes—
40#17988481C2218yes—
41#17988480C2218yes—
42#17988472C2218yescomplemented
43#17988471C2218yescomplemented
44#17988469C2218yescomplemented
45#17988468C2218yescomplemented
46#17988448C2218yes—
47#17988445C2218yes—
48C2×#14556498C2211yescharacteristic
49C2×#14556498C2211yescharacteristic
50C2×#14556498C2211yescharacteristic
51C2×#14556498C2211yescharacteristic
52C2×#14556498C2211yescharacteristic
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60C22×C4⋊C4×C73C2211yescharacteristic
61C22×C22⋊C4×C73C2211yescharacteristic
62C22×C22⋊C4×C73C2211yescharacteristic
63C22×C22⋊C4×C73C2211yescharacteristic
64C22×C42×C73C2211yescharacteristic
65#388×C73C2218yes—
66C2×#95×C73C2211yescharacteristic
67C2×#95×C73C2211yescharacteristic
68C22×Dic146—42no—
69C22×Dic146—42no—
70C22×Dic146C2×C418yes—
71C22×Dic146C2314yes—
72C23×Dic73—42no—
73C23×Dic73—42no—
74C23×Dic73C2×C418yes—
75C23×Dic73C2311yescharacteristic
76C23×Dic73C2311yescharacteristic
77C23×Dic73C2311yescharacteristic
78C23×Dic73C2311yescharacteristic
79C23×Dic73C2311yescharacteristic
80C23×Dic73C2311yescharacteristic
81C23×Dic73C2311yescharacteristic
82C23×Dic73C2311yescharacteristic
83C23×Dic73C2314yes—
84#14556568C2×C4164yescomplemented
85C2×C4⋊Dic73—42no—
86C2×C4⋊Dic73C2×C418yes—
87C2×C4⋊Dic73C2314yes—
88C2×C4⋊Dic73C2314yes—
89C2×#11924007—42no—
90C2×#11924007—42no—
91C2×#11924007—42no—
92C2×#11924007—42no—
93C2×#11924007C2×C418yes—
94C2×#11924007C2×C418yes—
95C2×#11924007C2314yes—
96C2×#11924007C2314yes—
97C2×#11924007C2314yes—
98C2×#11924007C2314yes—
99C2×#11924007C2314yes—
100C2×#11924007C2314yes—
101C2×C22⋊Dic73—42no—
102C2×C22⋊Dic73—42no—
103C2×C22⋊Dic73C2×C418yes—
104C2×C22⋊Dic73C2314yes—
105C2×C22⋊Dic73C2314yes—
106C2×C22⋊Dic73C2314yes—
107C2×C4×Dic73—42no—
108C2×C4×Dic73—42no—
109C2×C4×Dic73—42no—
110C2×C4×Dic73C2314yes—
111C2×C4×Dic73C2314yes—
112C2×C4×Dic73C2314yes—
113#14556498C2314yes—
114#14556498C2314yes—
115#14556498C2314yes—
116#14556498C2314yes—
117#14556498C2314yes—
118#14556498C2314yes—
119#14556498C2314yes—
120#14556498C2314yes—
121#14556498C2314yes—
122#14556498C2314yes—
123#14556498C2314yes—
124#14556498C2314yes—
125C25×C73C2311yescharacteristic
126C23×C4×C73C2311yescharacteristic
127C23×C4×C73C2311yescharacteristic
128C23×C4×C73C2311yescharacteristic
129C23×C4×C73C2311yescharacteristic
130C23×C4×C73C2311yescharacteristic
131C23×C4×C73C2311yescharacteristic
132C2×C4⋊C4×C73—42no—
133C2×C4⋊C4×C73C2314yes—
134C2×C22⋊C4×C73—42no—
135C2×C22⋊C4×C73—42no—
136C2×C22⋊C4×C73C2×C418yes—
137C2×C22⋊C4×C73C2314yes—
138C2×C22⋊C4×C73C2314yes—
139C2×C22⋊C4×C73C2314yes—
140C2×C42×C73—42no—
141C2×C42×C73C2314yes—
142#95×C73C2314yes—
143#95×C73C2314yes—
144C2×Dic146—416no—
145C2×Dic146—44no—
146C2×Dic146—44no—
147C2×Dic146C22×C4116yes—
148C22×Dic73—22no—
149C22×Dic73—22no—
150C22×Dic73—22no—
151C22×Dic73—22no—
152C22×Dic73—22no—
153C22×Dic73—22no—
154C22×Dic73—22no—
155C22×Dic73—22no—
156C22×Dic73—22no—
157C22×Dic73—22no—
158C22×Dic73—22no—
159C22×Dic73—22no—
160C22×Dic73—22no—
161C22×Dic73—22no—
162C22×Dic73—22no—
163C22×Dic73—22no—
164C22×Dic73—22no—
165C22×Dic73—22no—
166C22×Dic73—22no—
167C22×Dic73—22no—
168C22×Dic73—416no—
169C22×Dic73—44no—
170C22×Dic73—44no—
171C22×Dic73C22×C414yes—
172C22×Dic73C22×C414yes—
173C22×Dic73C22×C414yes—
174C22×Dic73C22×C414yes—
175C22×Dic73C22×C4116yes—
176C22×Dic73C2412yes—
177C22×Dic73C2412yes—
178C22×Dic73C2412yes—
179C22×Dic73C2412yes—
180C22×Dic73C2412yes—
181C22×Dic73C2412yes—
182C22×Dic73C2412yes—
183C22×Dic73C2412yes—
184C4⋊Dic73—44no—
185C4⋊Dic73C22×C4116yes—
186#11924007—44no—
187#11924007—44no—
188#11924007—44no—
189#11924007—44no—
190#11924007C22×C4116yes—
191#11924007C22×C4116yes—
192C22⋊Dic73—44no—
193C22⋊Dic73—44no—
194C22⋊Dic73C22×C4116yes—
195C4×Dic73—44no—
196C4×Dic73—44no—
197C4×Dic73—44no—
198C24×C73—22no—
199C24×C73—22no—
200C24×C73—22no—
201C24×C73—22no—
202C24×C73—22no—
203C24×C73—22no—
204C24×C73C22×C414yes—
205C24×C73C2412yes—
206C24×C73C2411yescharacteristic
207C22×C4×C73—22no—
208C22×C4×C73—22no—
209C22×C4×C73—22no—
210C22×C4×C73—22no—
211C22×C4×C73—22no—
212C22×C4×C73—22no—
213C22×C4×C73—22no—
214C22×C4×C73—22no—
215C22×C4×C73—22no—
216C22×C4×C73—22no—
217C22×C4×C73—22no—
218C22×C4×C73—22no—
219C22×C4×C73—22no—
220C22×C4×C73—22no—
221C22×C4×C73—22no—
222C22×C4×C73—22no—
223C22×C4×C73C22×C414yes—
224C22×C4×C73C22×C414yes—
225C22×C4×C73C2412yes—
226C22×C4×C73C2412yes—
227C22×C4×C73C2412yes—
228C22×C4×C73C2412yes—
229C22×C4×C73C2412yes—
230C22×C4×C73C2412yes—
231C4⋊C4×C73—44no—
232C22⋊C4×C73—44no—
233C22⋊C4×C73—44no—
234C22⋊C4×C73C22×C4116yes—
235C42×C73—44no—
236C23×C73—28no—
237C23×C73—28no—
238C23×C73—28no—
239C23×C73—22no—
240C23×C73—22no—
241C23×C73—22no—
242C23×C73—22no—
243C23×C73—22no—
244C23×C73—22no—
245C23×C73—44no—
246C23×C73—44no—
247C23×C73—44no—
248C23×C73—44no—
249C23×C73C23×C414yes—
250C23×C73C23×C412yes—
251C23×C73H(5,𝔽2)12yes—
252C23×C73H(5,𝔽2)12yes—
253C23×C73H(5,𝔽2)12yes—
254C23×C732−1+412yes—
255C23×C732−1+412yes—
256C23×C732−1+412yes—
257C23×C73C2511yescharacteristic
258C2×C4×C73—28no—
259C2×C4×C73—28no—
260C2×C4×C73—22no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—44no—
277C2×C4×C73—44no—
278C2×C4×C73—44no—
279C2×C4×C73—44no—
280C2×C4×C73C23×C414yes—
281C2×C4×C73C23×C414yes—
282C2×Dic73—28no—
283C2×Dic73—28no—
284C2×Dic73—28no—
285C2×Dic73—28no—
286C2×Dic73—22no—
287C2×Dic73—22no—
288C2×Dic73—22no—
289C2×Dic73—22no—
290C2×Dic73—22no—
291C2×Dic73—22no—
292C2×Dic73—22no—
293C2×Dic73—22no—
294C2×Dic73—22no—
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—416no—
307C2×Dic73—44no—
308C2×Dic73—44no—
309C2×Dic73—44no—
310C2×Dic73—44no—
311C2×Dic73C23×C414yes—
312C2×Dic73C23×C414yes—
313C2×Dic73C23×C414yes—
314C2×Dic73C23×C414yes—
315Dic146—416no—
316C22×C73—24no—
317C22×C73—24no—
318C22×C73—24no—
319C22×C73—416no—
320C22×C73—42no—
321C22×C73—42no—
322C22×C73—42no—
323C22×C73—42no—
324C22×C73#51814yes—
325C22×C73#51914yes—
326C22×C73#52014yes—
327C22×C73#56214yes—
328C22×C73#56214yes—
329C22×C73#56314yes—
330C22×C73#56314yes—
331C22×C73C24×C411yescharacteristic
332C22×C73C2×H(5,𝔽2)11yescharacteristic
333C22×C73C2×H(5,𝔽2)11yescharacteristic
334C22×C73C2×H(5,𝔽2)11yescharacteristic
335C22×C73C2×2−1+411yescharacteristic
336C22×C73C2×2−1+411yescharacteristic
337C22×C73C2×2−1+411yescharacteristic
338C4×C73—24no—
339C4×C73—24no—
340C4×C73—42no—
341C4×C73—42no—
342C4×C73—42no—
343C4×C73—42no—
344Dic73—24no—
345Dic73—24no—
346Dic73—24no—
347Dic73—24no—
348Dic73—42no—
349Dic73—42no—
350Dic73—42no—
351Dic73—42no—
352C2×#2378—731nomaximal, Sylow
353C2×C73—44no—
354C2×C73#237818yescomplemented
355C2×C73C2×#51811yescharacteristic
356C2×C73C2×#51911yescharacteristic
357C2×C73C2×#52011yescharacteristic
358C2×C73C2×#56211yescharacteristic
359C2×C73C2×#56211yescharacteristic
360C2×C73C2×#56311yescharacteristic
361C2×C73C2×#56311yescharacteristic
362C22×C22⋊Q8—731no—
363#2378—7316no—
364C2×#391—731no—
365C2×#391—731no—
366C2×#389—731no—
367C2×#389—731no—
368C2×#388—731no—
369C2×#388—731no—
370C2×#388—731no—
371C2×#388D7311yescharacteristic
372C2×#387—731no—
373C2×#387—731no—
374C2×#387—731no—
375C2×#387—731no—
376C2×#381—731no—
377C2×#380—731no—
378C73C2×#237811yescharacteristic, complemented, Sylow
379C23×Q8—731no—
380C24×C4—731no—
381C2×C22⋊Q8—7316no—
382C2×C22⋊Q8—738no—
383C22×C4⋊C4—731no—
384C22×C4⋊C4—731no—
385C22×C4⋊C4—731no—
386C22×C4⋊C4—731no—
387C22×C4⋊C4—731no—
388C22×C4⋊C4—731no—
389C22×C4⋊C4—731no—
390C22×C4⋊C4—731no—
391C22×C4⋊C4C2×D7311yescharacteristic
392C22×C22⋊C4—731no—
393C22×C22⋊C4—731no—
394C22×C22⋊C4—731no—
395C22×C22⋊C4C2×D7311yescharacteristic
396C22×C22⋊C4C2×D7311yescharacteristic
397C22×C22⋊C4C2×D7311yescharacteristic
398C22×C42—731no—
399C22×C42—731no—
400C22×C42—731no—
401C22×C42C2×D7311yescharacteristic
402#391—738no—
403#391—738no—
404#389—738no—
405#389—738no—
406#388—738no—
407#388—738no—
408#388—738no—
409#388C2×D7318yes—
410#387—738no—
411#387—738no—
412#387—738no—
413#387—738no—
414#381—738no—
415#380—738no—
416C2×#95—731no—
417C2×#95—731no—
418C2×#95—731no—
419C2×#95—731no—
420C2×#95—731no—
421C2×#95—731no—
422C2×#95—731no—
423C2×#95—731no—
424C2×#95—731no—
425C2×#95—731no—
426C2×#95—731no—
427C2×#95—731no—
428C2×#95C2×D7311yescharacteristic
429C2×#95C2×D7311yescharacteristic
430C25C22×D7311yescharacteristic
431C22×Q8—2922no—
432C22×Q8—2922no—
433C22×Q8—738no—
434C22×Q8—734no—
435C23×C4—2922no—
436C23×C4—2922no—
437C23×C4—738no—
438C23×C4—734no—
439C23×C4—731no—
440C23×C4—731no—
441C23×C4—731no—
442C23×C4—731no—
443C23×C4—731no—
444C23×C4—731no—
445C23×C4—731no—
446C23×C4—731no—
447C23×C4C22×D7311yescharacteristic
448C23×C4C22×D7311yescharacteristic
449C23×C4C22×D7311yescharacteristic
450C23×C4C22×D7311yescharacteristic
451C23×C4C22×D7311yescharacteristic
452C23×C4C22×D7311yescharacteristic
453C22⋊Q8—7364no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—2922no—
456C2×C4⋊C4—2922no—
457C2×C4⋊C4—2922no—
458C2×C4⋊C4—2922no—
459C2×C4⋊C4—2922no—
460C2×C4⋊C4—734no—
461C2×C4⋊C4—734no—
462C2×C4⋊C4—734no—
463C2×C4⋊C4—734no—
464C2×C4⋊C4—734no—
465C2×C4⋊C4—738no—
466C2×C4⋊C4—738no—
467C2×C4⋊C4—738no—
468C2×C4⋊C4—734no—
469C2×C4⋊C4—734no—
470C2×C4⋊C4—734no—
471C2×C4⋊C4C22×D7314yes—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—2922no—
475C2×C22⋊C4—2922no—
476C2×C22⋊C4—734no—
477C2×C22⋊C4—734no—
478C2×C22⋊C4—738no—
479C2×C22⋊C4—734no—
480C2×C22⋊C4C4×D7318yes—
481C2×C22⋊C4C22×D7314yes—
482C2×C22⋊C4C22×D7314yes—
483C2×C22⋊C4C22×D7314yes—
484C2×C42—42no—
485C2×C42—2922no—
486C2×C42—2922no—
487C2×C42—2922no—
488C2×C42—734no—
489C2×C42—734no—
490C2×C42—734no—
491C2×C42C22×D7314yes—
492#95—734no—
493#95—734no—
494#95—734no—
495#95—734no—
496#95—734no—
497#95—734no—
498#95—734no—
499#95—734no—
500#95—734no—
501#95—734no—
502#95—734no—
503#95—734no—
504#95C22×D7314yes—
505#95C22×D7314yes—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24C2×C4×D7314yes—
513C24C23×D7312yes—
514C24C23×D7311yescharacteristic
515C2×Q8—2924no—
516C2×Q8—2924no—
517C2×Q8—29216no—
518C2×Q8—7316no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—2924no—
536C22×C4—2924no—
537C22×C4—29216no—
538C22×C4—7316no—
539C22×C4—734no—
540C22×C4—734no—
541C22×C4—734no—
542C22×C4—734no—
543C22×C4—732no—
544C22×C4—732no—
545C22×C4—732no—
546C22×C4—732no—
547C22×C4—732no—
548C22×C4—732no—
549C22×C4—732no—
550C22×C4—732no—
551C22×C4—1462no—
552C22×C4—1462no—
553C22×C4—1462no—
554C22×C4—1462no—
555C22×C4—1462no—
556C22×C4—1462no—
557C22×C4—1462no—
558C22×C4—1462no—
559C22×C4—1462no—
560C22×C4—1462no—
561C22×C4—1462no—
562C22×C4—1462no—
563C22×C4—1462no—
564C22×C4—1462no—
565C22×C4—1462no—
566C22×C4—1462no—
567C22×C4—1462no—
568C22×C4—1462no—
569C22×C4—1462no—
570C22×C4—1462no—
571C22×C4C2×C4×D7314yes—
572C22×C4C2×C4×D7314yes—
573C22×C4C23×D7312yes—
574C22×C4C23×D7312yes—
575C22×C4C23×D7312yes—
576C22×C4C23×D7312yes—
577C22×C4C23×D7312yes—
578C22×C4C23×D7312yes—
579C4⋊C4—44no—
580C4⋊C4—2924no—
581C4⋊C4—2924no—
582C4⋊C4—2924no—
583C4⋊C4—2924no—
584C4⋊C4—2924no—
585C4⋊C4—7316no—
586C4⋊C4—7316no—
587C4⋊C4—7316no—
588C22⋊C4—44no—
589C22⋊C4—44no—
590C22⋊C4—2924no—
591C22⋊C4—2924no—
592C22⋊C4—7316no—
593C22⋊C4C2×C4×D73116yes—
594C42—44no—
595C42—2924no—
596C42—2924no—
597C42—2924no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—28no—
605C23—28no—
606C23—28no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23C22×C4×D7314yes—
612C23C22×C4×D7312yes—
613C23#1455663612yes—
614C23#1455663612yes—
615C23#1455663712yes—
616C23#1455663812yes—
617C23#1455663812yes—
618C23#1455663812yes—
619C23C24×D7311yescharacteristic
620Q8—29216no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—28no—
626C2×C4—28no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—2924no—
644C2×C4—2924no—
645C2×C4—2924no—
646C2×C4—2924no—
647C2×C4—29216no—
648C2×C4—734no—
649C2×C4—734no—
650C2×C4—734no—
651C2×C4—734no—
652C2×C4—1462no—
653C2×C4—1462no—
654C2×C4—1462no—
655C2×C4—1462no—
656C2×C4—1462no—
657C2×C4—1462no—
658C2×C4—1462no—
659C2×C4—1462no—
660C2×C4—1462no—
661C2×C4—1462no—
662C2×C4—1462no—
663C2×C4—1462no—
664C2×C4—1462no—
665C2×C4—1462no—
666C2×C4—1462no—
667C2×C4—1462no—
668C2×C4—1462no—
669C2×C4—1462no—
670C2×C4—1462no—
671C2×C4—1462no—
672C2×C4—1468no—
673C2×C4—1468no—
674C2×C4—1468no—
675C2×C4—1468no—
676C2×C4C22×C4×D7314yes—
677C2×C4C22×C4×D7314yes—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—416no—
686C22#1798905914yes—
687C22#1798906414yes—
688C22#1798906614yes—
689C22#1798933114yes—
690C22#1798933214yes—
691C22#1798933914yes—
692C22#1798934014yes—
693C22C23×C4×D7311yescharacteristic
694C22C2×#1455663611yescharacteristic
695C22C2×#1455663611yescharacteristic
696C22C2×#1455663711yescharacteristic
697C22C2×#1455663811yescharacteristic
698C22C2×#1455663811yescharacteristic
699C22C2×#1455663811yescharacteristic
700C4—24no—
701C4—24no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—2922no—
707C4—2922no—
708C4—2922no—
709C4—2922no—
710C4—1464no—
711C4—1464no—
712C4—1464no—
713C4—1464no—
714C2—44no—
715C2#2261309818yesdirect product factor
716C2C2×#1798905911yescharacteristic
717C2C2×#1798906411yescharacteristic
718C2C2×#1798906611yescharacteristic
719C2C2×#1798933111yescharacteristic
720C2C2×#1798933211yescharacteristic
721C2C2×#1798933911yescharacteristic
722C2C2×#1798934011yescharacteristic
subgroupG/H
centerC24C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC2×#388×C73C2
socleC24×C73C24
prime radicalC25×C73C23
cosocleC23×C73C25
hypercenterC2×#388D73
hypocenterC73C2×#2378
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#388

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #22613098C2direct (N × H)
3. C2×#17988493C2semidirect
4. C2×#17988491C2semidirect
5. C2×#17988484C2semidirect
6. C2×#17988483C2semidirect
10. C2×#17988472C2semidirect
11. C2×#17988471C2semidirect
12. C2×#17988469C2semidirect
13. C2×#17988468C2semidirect
19. C2×#14556568C4semidirect
35. #17988493C22semidirect
36. #17988491C22semidirect
37. #17988484C22semidirect
38. #17988483C22semidirect
42. #17988472C22semidirect
43. #17988471C22semidirect
44. #17988469C22semidirect
45. #17988468C22semidirect
84. #14556568C2×C4semidirect
354. C2×C73#2378semidirect
378. C73C2×#2378semidirect
715. C2#22613098direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#145565682
#226130982
C2×#179884932
C2×#179884912
C2×#179884842
C2×#179884832
C2×#179884812
C2×#179884802
C2×#179884722
C2×#179884712
C2×#179884692
C2×#179884682
C2×#179884482
C2×#179884452
C2×#388×C732
C2×#237873